Christopher Steele, the former British spy, had repeated contacts before and after the election with F.B.I. counterintelligence agents who were investigating links between the Trump campaign and Russians.CreditCreditVictoria Jones/Press Association, via Associated Press

WASHINGTON — More than a year after Republican leaders promised to investigate Russian interference in the presidential election, two influential Republicans on Friday made the first known congressional criminal referral in connection with the meddling — against one of the people who sought to expose it.

Senator Charles E. Grassley of Iowa, the chairman of the Judiciary Committee, and Senator Lindsey Graham of South Carolina, a senior committee member, told the Justice Department that they had reason to believe that a former British spy, Christopher Steele, lied to federal authorities about his contacts with reporters regarding information in a dossier, and they urged the department to investigate. The committee is running one of three congressional investigations into Russian election meddling, and its inquiry has come to focus on, in part, Mr. Steele’s explosive dossier that purported to detail Russia’s interference and the Trump campaign’s complicity.

The decision by Mr. Grassley and Mr. Graham to single out the former intelligence officer behind the dossier infuriated Democrats and raised the stakes in the growing partisan battle over the investigations into Mr. Trump, his campaign team and Russia.

The Senate Judiciary Committee effort played into a far broader campaign waged by conservatives to cast doubt on the Trump-Russia investigations, and instead turn the veracity of the dossier and the credibility of its promulgators into the central issue. At the same time, President Trump and his allies have demanded that the Justice Department reopen its investigation of Hillary Clinton’s email server and the Clinton Foundation. F.B.I. agents have begun interviewing people connected to the foundation about whether any donations were made in exchange for political favors while Mrs. Clinton was secretary of state.

Beyond the Senate Judiciary Committee, Representative Devin Nunes of California, the chairman of the House Intelligence Committee, has also been pressing to train focus of its Russia investigation on the dossier. This week, he appeared to finally secure access to F.B.I. documents and witnesses that he views as crucial to unraveling what the bureau did with the dossier. And he has aggressively pursued Fusion GPS, the research firm that hired Mr. Steele — the committee, for instance, has issued only a single subpoena in its investigation for bank records, those of Fusion GPS.

More than a year ago, Republican leaders in Congress agreed that committees in the House and Senate would investigate Russia’s efforts to influence the outcome of the 2016 election. Mr. Graham declared in December 2016, “The first thing we want to establish is, ‘Did the Russians hack into our political system?’ Then you work outward from there.”

Since then, that spirit of bipartisanship has frayed. At this point, only the Senate Intelligence Committee appears to be pursuing an investigation with bipartisan support. But Mr. Grassley said he did only what he had to.

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Two Republican senators on the Judiciary Committee formally recommended criminal charges against Christopher Steele in connection with their Russia investigation.

“I don’t take lightly making a referral for criminal investigation,” he said. “But, as I would with any credible evidence of a crime unearthed in the course of our investigations, I feel obliged to pass that information along to the Justice Department for appropriate review.”

Democrats were furious.

“It’s clearly another effort to deflect attention from what should be the committee’s top priority: determining whether there was collusion between the Trump campaign and Russia to influence the election and whether there was subsequent obstruction of justice,” said Senator Dianne Feinstein of California, the top Democrat on the Judiciary Committee, who added that she had not been consulted about the referral.

The criminal referral makes no assessment of the veracity of the dossier’s contents, much of which remains unsubstantiated nearly a year after it became public.

But the dossier has emerged as Exhibit A in Republicans’ insistence that Obama-era political bias could have affected the F.B.I.’s decision to open a counterintelligence investigation in July 2016 into whether Mr. Trump’s associates aided the Russian election interference.

Republicans, including the two senators, have argued that the dossier is tantamount to political opposition research, and claimed that it might have been used by the F.B.I. to open its investigation. They have also said it might have provided the basis for key investigative actions, including a secret court-approved wiretap of a Trump campaign aide.

Current and former American and foreign officials with direct knowledge of the investigation say that the federal inquiry did not start with the dossier, nor did it rely on it. Rather, they have said, the dossier and the F.B.I.’s discussions with Mr. Steele merely added material to what American law enforcement and spy agencies were gleaning from other sources.

Mr. Grassley’s decision to recommend a criminal investigation appeared likely to be based on reports of Mr. Steele’s meetings with the F.B.I., which were provided to the committee by the Justice Department in recent weeks.

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Senator Charles E. Grassley of Iowa, who heads the Judiciary Committee, is overseeing an array of inquiries related to the the F.B.I. and its investigations of both Hillary Clinton and the Trump campaign.CreditTom Brenner/The New York Times

It was not clear why, if a crime is apparent in the F.B.I. reports that were reviewed by the Judiciary Committee, the Justice Department had not moved to charge Mr. Steele already. The circumstances under which Mr. Steele is alleged to have lied were unclear, as much of the referral was classified.

Two Trump associates — Michael T. Flynn, the former national security adviser, and George Papadopoulos, a former campaign aide — have pleaded guilty to lying to the F.B.I. in the investigation led by the special counsel, Robert S. Mueller III.

Though Mr. Grassley made no mention of the two men on Friday, he appeared to suggest equivalence between their crimes and his views of Mr. Steele’s actions. “If the same actions have different outcomes, and those differences seem to correspond to partisan political interests, then the public will naturally suspect that law enforcement decisions are not on the up-and-up,” he wrote.

In a short cover letter dated Thursday but transmitted Friday, the senators wrote, “Based on the information contained therein, we are respectfully referring Mr. Steele to you for investigation of potential violations of 18 U.S.C. § 1001, for statements the Committee has reason to believe Mr. Steele made regarding his distribution of information contained.”

That section of the federal criminal code refers to knowingly making false or misleading statements to federal authorities.

Mr. Steele had repeated contacts before and after the election with F.B.I. counterintelligence agents who were investigating links between the Trump campaign and Russians. The information he shared was apparently valuable enough that the F.B.I. at one point even considered bringing him on as a paid source. They backed off the idea only after the dossier became public in January 2017 and Mr. Steele’s identity became widely known, leading the bureau to conclude that he would no longer be able to function as a source for its investigation.

More recently, Mr. Steele has been in contact with Mr. Mueller, who took over the investigation last year.

Anyone can make a criminal referral to the Justice Department, which is not obligated to take up the matter. But a recommendation from a senior senator who runs the committee that has oversight of the department comes with added weight.

The Justice Department had no immediate comment on the referral. But Fusion GPS characterized the recommendation to charge Mr. Steele as a smear and an attempt to further muddy the inquiry into Russia’s interference.

“Publicizing a criminal referral based on classified information raises serious questions about whether this letter is nothing more than another attempt to discredit government sources, in the midst of an ongoing criminal investigation,” said Joshua A. Levy, the lawyer for Fusion GPS. “We should all be skeptical in the extreme.”

Mr. Grassley is overseeing an array of inquiries related to the F.B.I. and its investigations of both Mrs. Clinton and the Trump campaign. He and Mr. Graham have repeatedly pressed the agency on its handling of the dossier, in particular, and fought to gain access to key agency witnesses and documents about the matter, reviewing a large tranche of such material in recent weeks.

Fusion GPS hired Mr. Steele, a former officer of Britain’s MI6 with deep connections in Russia, during the spring of 2016 to research Mr. Trump’s ties to Russia. His findings were ultimately compiled into 35 pages of memos outlining a multipronged conspiracy between the Russian government and the Trump campaign to boost his candidacy and hurt Mrs. Clinton, including corrupt business dealings and salacious details alleging an encounter between Mr. Trump and Russian prostitutes.

This week has seen Mr. Grassley engage in a heated spat with Fusion GPS over the testimony of one of its executives, Glenn R. Simpson. It began when Mr. Simpson and his partner, Peter Fritsch, published an op-ed article in The New York Times accusing Republicans of waging “a cynical campaign” to try to discredit the firm and its findings and calling on the relevant congressional committees to release transcripts of a series of closed-door interviews with the men.

A spokesman for Mr. Grassley, Taylor Foy, shot back, saying that Mr. Simpson had declined to provide public testimony or additional documents and answers requested after the interview.